Recently New Feature: real time updates to questions, answers, and inbox was implemented. With this feature the amount of questions with new activity is shown in parenthesis at the beginning of the page title, e.g.
(2) Meta Stack Overflow
means that MSO has two questions with new activity since the user last viewed it.
As noted by Kip this feature is unrelated to inbox updates. Here is an example to illustrate this:
Even though there are two inbox messages in this screenshot this is not reflected by the page title. The page title is currently only sensitive to questions with new activity.
I suggest that the page title also reflects inbox updates. For the screenshot above this would mean that the page title shows that there are two inbox updates and two questions with new activity.
I am not sure what format is best for showing this. For chat * in the page title is used to show that there are messages directed at you which is similar in meaning to inbox updates. However, * if is placed after the number in parenthesis to denote inbox updates there might be confusion as there is no connection between the number in parenthesis and * like in chat. Thus, one might prefer another format such as one of the following (all are meant to reflect the status of the screenshot above):
* (2) Meta Stack Overflow
2* (2) Meta Stack Overflow
 (2) Meta Stack Overflow
2i 2q Meta Stack Overflow
(2/2) Meta Stack Overflow
(2|2) Meta Stack Overflow
For the alternatives without an explicit hint of which number refers to what it might be best to place the number for questions with new activity first as it will in most cases be greater. This will to a greater degree avoid combinations such as "(0/2)" which may be confused zero of two.
An advantage of the suggested feature is that if the user has a browser tab with a Stack Exchange site then they will be instantly notified of inbox updates. They do not need to focus a tab with a Stack Exchange site to know if there are inbox updates, they merely have to check the relevant page titles among their tabs.
A disadvantage of the suggested feature is that it might be experienced as verbose. I suggest that it is implemented such that it is as unobtrusive as possible while still being informative. Think of a situation where a user has
one Meta Stack Overflow tab with two inbox updates relating to Meta Stack Overflow and two questions with new activity, and
one Super User tab with one inbox updates relating to Super User and three questions with new activity.
Then the sum of the inbox notification in the page titles should be local to sites and not global. The page titles for the tabs above should be something like the following pair:
2i 2q Meta Stack Overflow
1i 3q Super User